Computing apparatus for performing multiplication and division



June 7, 1966 M. H. F.- GlOT ETAL 3,

COMPUTING APPARATUS FOR PERFORMING MULTIPLICATION AND DIVISION FiledApril 20, 1962 5 Sheets-Sheet 1 S! co (9o (I) R i o i I T I T 8 u-INVENTORS MAURICE HENRI FERNAND GIOT M BERNARD JOBART W CHARLES ROGERFEVROT TJEAN MEYER n BY g -,c,4. ,fl-ob$aw JW ATTORNEYS June 7, 1966 M.H. F. GIO'I ETAL 3,255,340

COMPUTING APPARATUS FOR PERFORMING MULTIPLICATION AND DIVISION 5Sheets-Sheet 2 Filed April 29 1962 w w W N R 7 5mm Q WET TFRR mm M wm mammmu mu t m m ow macd M J f I B Q NJ M N %& 3 1m 1. m 1. Do m w m o O oO o m. em T w. .w m cm am on wm Q om Wm #NWH N 0| mm v N m. on mkm 0M 0wcoll. hl momo fio i ome fi v m 00 00 a 00 0O 0'' 0o o w w ATTORNEYS June7, 1966 M. H. F. GIOT ETAL COMPUTING APPARATUS FOR PERFORMINGMULTIPLICATION AND DIVISION 5 Sheets-Sheet 3 Filed April 20, 1962INVENTORS MAURICE HENRI FERNAND GIOT BERNARD JOBART CHARLES ROGER FEVROTJEAN MEYER ATTORN EY;

June 7, 1966 M. H. F. GIOT ETAL COMPUTING APPARATUS FOR PERFORMINGMULTIPLICATION AND DIVISION Filed April 20 1962 5 Sheets-Sheet 4.

FIG. 4

ATTORNEYS June 7, 1966 M. H. F. GIOT ETAL 3,255,340

COMPUTING APPARATUS FOR PERFORMING MULTIPLICATION AND DIVISION FiledApril 20, 1962 s Sheets-Sheet s INVENTORS MAURICE HENRI FERNAND GIOTBERNARD JOBART CHARLES ROGER FEVROT JEAN MEYER ATTORNEYS 8. mm E womDommwJDm BY (WW D WQL m o @o m 6 0 0 oo @o o 5.0 dd 00 United States PatentClaims. (or. 235-160) The present invention pertains to electricalapparatus for performing the multiplication or division of a givenpredetermined number by a simple predetermined factor with the aid ofelectric switches whose number and arrangement are determined as afunction of the said multiplication or division factor.

The apparatus according to the present invention comprises at least asmany groups of switches as the number to be multiplied or divided maycomprise digits, and each such group is allocated to a separate order,viz. units, tens, etc., in that number. The switches of each group arecontrolled by a single organ which serves to define or set up the valueof the digit in the correspondin order of the multiplicand or dividend.The switches are ten-position switches when the apparatus is to be usedfor operation with decimal numbers; they possess n positions when usedwith a number system of the base n. Each group of switches includes whatmay be called a principal switch for setting and if desired foreffecting display of one of the constituent digits of the number to bemultiplied or divided. Each group further includes one or more auxiliaryswitches coupled to the principal switch in such a way as to define ordisplay a terminal or number corresponding to the desired multiple orsubmultiple of the digit identified or defined by the said principalswitch.

In an operation of multiplication or division by a simple factor, thedigits of the product or quotient number resulting from multiplicationor division of the multi plicand or dividend by the saidfactor are theresultant of the addition of the last digit of the operation effected bythe factor on the digit of same arithmetic order in the number to bemultiplied or divided and of the carry resulting from the operationeffected on the digit of adjacent order. To give an example:

which may be written thus:

Consequently in each group each auxiliary switch is connected to one ormore auxiliary switches of the adjacent higher or lower order, accordingas the operation being performed is one of multiplication or division,in order to effect transfer of the carry.

The switches may for example take the form of rotary switches whosecentral terminals are put into electrical contact with peripheralterminals by means of rotating indices or wiper arms. The indices in asingle group are mounted on a common axis controlled by any suitablemeans such as a handle so that all indices will possess the samerotational position.

- results:

The apparatus according to the invention may be constructed to operateeither by means of electric current (alternatingor direct), the switchesefiectuating within each group and from group to group the necessaryelectrical connections, or by means of pulses. When pulses are employed,the switches are used not to display the digits resulting from theoperation effected by the factor but to direct toward pulsetotalizators, via as many channels as there are digits in themultiplicand number, a number of electric pulses equal to the value ofeach on of those digits.

The invention will now be further described with reference to theaccompanying drawings in which:

FIGURE 1 is a schematic representation of apparatus according to theinvention for multiplying by the factor two.

FIGURE 2 is a schematic representation of apparatus according to theinvention for multiplying by three.

FIGURE 3 is a schematic representationof apparatus according to theinvention for effecting division by two.

FIGURE 4 is a schematic diagram of apparatus according to the inventionfor dividing by three.

FIGURE 5 represents a modification of the apparatus of FIGURE 3operating by means of pulses.

For simplification in the drawings the principal switches are not showncoupled to any means for display of the multiplicand number digits whichthey define. Their function is solely a function of indication and notof switching. They will nonetheless hereinafter be described asprincipal switches because they may be used as electric switches, e.g.,for a display or monitoring function, without departure from theinvention.

FIGURE 1 shows a device for effecting multiplication by two. Thisapparatus includes one set of switches per arithmetic order. Thus forexample there is a switch group C.U. for units, a group CD. for decadesor tens and a group CC. for hundreds. comprises a principal switch,shown at G; for the units C.U., at 6' for the tens CD, and at G, for thehundreds C.C. Each group further comprises one or more auxiliaryswitches such as those indicated at G G G 'G" G" etc. Each group furtherincludes an interconnection switch as indicated at G G' and G",,.

The various digits which make up the number to be multiplied by two,i.e., the digits of the multiplicand, are set up in the exampleillustrated in FIGURE 1 by manipulation of the principal switch G forthe units, (3' for the tens, G" for the hundreds and so on.

The difierent principal switches 6,, 6' G" etc. hence include positionsfor the values zero, one, two, three, four, five, six, seven, eight,nine. These are the numbers whose multiplication by 2 gives thefollowing Consequently the switches G and G of a single group areassociated in the following manner;

To the position 0 of G there corresponds-the display 0 at G2 5 To theposition 1 of G there corresponds the display 2 at G2 Each group.

To the position 2 of G there corresponds the display 4 at G2 To theposition 3 of G at G2 To the position 4 of G at G2 To the position 5 ofG at G2 To the position 6 of G at G2 To the position 7 of G at G2 To theposition 8 of G at G2 To the position 9 of G there corresponds thedisplay 8 at G2 The remainder or carry 10 occurring upon multiplicationby two at each of the last five positions of the principal switch G istransmitted to the group of switches of the adjacent higher order insuch a fashion that to the number defined by the principal switch G ofthe said group of adjacent higher order there corresponds the numberdefined by the associated auxiliary switch G' increased by 1, thisnumber appearing at G' To this end the switches G and G; of a singlegroup (above that of lowest order) are associated in the followingmanner:

To the position 0 of G there corresponds the display of 1 at G (i.e.,value of G +1) To the position 1 of G there corresponds the display of 3at G (i.e., value of G +1) To the position 2 of G there corresponds thedisplay of 5 at G (i.e., value of G +1) To the position 3 of G therecorresponds the display of 7 at G, (i.e., value of G -l-l) To theposition 4 of G there corresponds the display of 9 at G (i.e., value ofG +1) To the position 5 of G there corresponds the display of l at G(i.e., value of 6 -1-1) To the position 6 of G there corresponds thedisplay of 3 at 6,; (i.e., value of G +1) To the position 7 of G therecorresponds the display of 5 at G (i.e., value of G +l) To the position8 of G there corresponds the display of 7 at G (i.e., value of G +l) Tothe position 9 of G there corresponds the display of 9 at G (i.e., valueof 6 1) In the foregoing table, G is the first auxiliary switch in theorder containing the switches G and G of the table, the primes havingbeen omitted. In the figures, single primes denote the second order anddouble primes denote the third order.

The auxiliary switches G' G" are energized only when there is noremainder or carry deriving from the group of switches of the adjacentlower order, a condition that occurs only for the first five numbers,zero, one, two, three, four, of the principal switch in the saidadjacent lower order.

In consequence the group of switches C.U. is connected electrically tothe auxiliary switch G' of CD. only for the O, 1, 2, 3, 4 positions of Gthe connection being effected by means of the first five terminals onthe auxiliary interconnection switch G For the five last positions 5, 6,7, 8 and 9 of G the switch group of the units order C.U. is connected tothe switch G' of the tens order CD. by means of the last five terminalson the auxiliary interconnection switch G the number displayed by theswitch G';, in OD. being the same as that displayed by G in CD.increased by the carry one.

The operation of the apparatus is as follows:

If the number to be multiplied by 2 is 094 for example the digit 4 isset up in the units switch group C.U. where there corresponds thedisplay 6 there corresponds the display 8 there corresponds the display0 there corresponds the display 2 there corresponds the display 4 therecorresponds the display 6 A} it is displayed by means of the principalswitch G Similarly in the tens and hundreds orders respectively thedigit 9 is set up by means of the principal switch G' and the digit 0 isset up by means of the principal switch G The rotating wipers on theswitches being mounted on a common axis within each group, the wipers ofthe switches G and G in the units order and correspondingly of theswitches G 6' and G' in the tens order and G G and G in the hundredsorder talre positions corresponding to the positions of G G' and G"respectively.

To the fifth position (labeled 4) of G in C.U. there corresponds theterminal or display 8 on switch G and the fifth terminal on switch G Thetwo terminals of the lamp connected to terminal 8 of switch G in theunits order are therefore connected to two poles of a source ofpotential difference and this lamp will light, displaying the number 8.

To the tenth position 9 of G' in the tens order C.D. there correspondsthe terminal-or display 8 on G' also terminal or display 9 on G and thetenth terminal on G' Theswitch G is energized via the fifth terminal onG whereas the switch G is not energized. Hence the lamp connected toterminal 8 on G' will be lighted, exhibiting the number 8, whereas thelamp connected to terminal 9 on G' will not be lighted.

To the first position 0 and G" there correspond the terminals ordisplays 0 on G 1 on G';; and, in case there is a group of switches forthe thousands order, the first terminal on G If there is not, the firstfive terminals on G" are without connection, the last five beingconnected to one of the terminals of a lamp for display of the number 1,of which the other terminal connects to one of the poles of the sourceof current. The auxiliary switch G" is not fed by the interconnectionswitch G since, as shown in FIGURE 1, G is in its tenth position. 011the other hand the switch G" is energized, hence the lamp connected tothe first terminal on G is energized and the digit 1 on G" will bedisplayed.

The result displayed is hence 188, which is double the values of 094.

Referring again to FIGURE 1, the two terminals of a source of potentialdifference are shown at conductors 2 and 4. Conductor 4 connects, via anon-off switch 6 for the entire apparatus of FIGURE 1, with a conductor8. The apparatus of FIGURE 1 further includes a plurality of gangedswitches of which three are shown generally at 10, 12 and 14. Theseswitches are respectively allocated to the units, tens and hundredsorders of the m ulti-digit multiplicand numbers which are, in

the apparatus of FIGURE 1, to be multiplied by two. For higher orderdigits of the multiplicand additional switches similar to switch 14 maybe provided in FIG- URE 1 to the left of switch 14.

Each of switches 10, 12 and 14 includes a plurality of decks orindividual ten position switches ganged together. One deck, sometimesherein called a principal switch, and identified at G G and G" in theswitches 10, 12 and 14 respectively, may include simply a pointer 16movable to ten positions numbered 0 to 9. These positions may be definedby mechanical detent elements 17. If desired, indicator lamps may beprovided for the display of the digits thus selected by the pointers 16,the pointers then serving a switching function to energize the indicatorlamps at the positions to which the pointers are set. Setting of thepointers may be manually eifected.

A second deck in switch 10 is identified at G and is sometimes hereincalled an auxiliary switch. Two similar second decks are provided ineach of the switches 12 and 14, identified at G G' and at G and G" Eachof these second decks includes ten stationary terminals 20 and a movablewiper contact 18. The sta-.

V tionary contacts 20 lead through individual lamps 22 to the conductor2. nects to conductor 8.

Each of switches 10, 12 and 14 includes a third deck, sometimes hereincalled a transfer switch, and identified at G G' and G in switches 10,12 and 14 respectively. Each of these third decks includes tenstationary terminals 24 and a movable wiper con-tact 26. The wipercontacts 26 connect with conductor 8. The first five stationary contacts24 connect in parallel to the wiper 18 of the first auxiliary switch ofadjacent higher order, while the second five stationary contacts 24connect in parallel to the wiper 18 of the second auxiliary switch ofadjacent higher order. Thus the first five terminals 24 of deck G inswitch connect to wiper 18 of deck G while the last five terminals 24 ofdeck G connect to wiper 18 of deck G' The first five and last fiveterminals of deck G in switch 12 similarly connect respectively to thewipers 18 of decks G" and G} in switch 14.

The indicator lamps 22 have painted thereon or otherwise associatedtherewith indicia as indicated by the numbers shown, in FIGURE 1, withinthe circles which represent these indicator lamps. In decks G G' and G";of switches 10, 12 and 14 these indicia are the lowest order digits ofthe numbers (Whether one-digit or twodigit) which equal respectively theproducts of the numbers 0 to 9 multiplied by two. In decks G' and G" ofswitches 12 and 14, these indicia are, at corresponding terminals 22,the same as the indicia in decks 6' and G increased by unity.

In each of switches 10, 12 and 14, the pointer 16 and all wipers 18 and26 are fixed relative to each other and occupy the same angularposition. Thus, for determination of the product of any three-digitnumber and two, it is only necessary to set up the digits of that numberon the switches 10, 12 and 14 beginning at switch 10 with the digit oflowest order, and the product may be read ofi from the illuminated lampsin the decks G" or G G;; or G and G Since the product Will, formultiplicands of value above 499, include a digit in the fourth order,provision must be made for display of this fourth order product digit.If only three ganged switches 10, 12 and 14 are provided, this fourthorder digit can have only the value unity, and display thereof isprovided for by connecting the last five terminals'24 on deck G" to oneside of a lamp 28, the other side of which leads to conductor 2. Thislamp may be arranged to display the number one. The first five terminals24 of G" may be suppressed in such an embodiment.

It is evident that the apparatus schematically shown In switch 10, wiperarm 18 conin FIGURE 1 may be extended to any number of digits.

The apparatus represented schematically in FIGURE 2 is so constructed asto effect multiplication by three. It is analogous to that shown inFIGURE 1, differing only in that it requires a larger number ofauxiliary switches since the carries to be taken care of are either onor two.

In the same fashion as in FIGURE 1 and for simpli cation of the figurethe principal switches possess in FIGURE 2 no electrical function.Rather they areprovided only for set up and indication of the value ofthe multiplicand digits. Moreover, and again for purposes ofsimplification, the lamps connected to the terminals of the auxiliaryswitches and fed by those terminals for display of the product or answerdigits have not been shown. It is to be assumed in the descriptionfollowing that each time a terminal is energized on any of the auxiliaryswitches G G G" G' G G2 G" the corresponding lamp will be illuminatedfor display of an answer digit by illumination of an indicium associatedwith that lamp.

The different principal switches 6,, 6' G possess each ten positions forthe multiplicand digit numbers 6 0, l, 2, 3, 4, 5, 6, 7, 8, 9, whosemultiplication by 3 produces the following products:

To position 0 on G the number displayed at G will be 0 To position 1 onG the number displayed at G will be 3 To position 2 on G the numberdisplayed at G will be 6 .To position 3 on G the number displayed at Gwill be 9 To position 4 on G the number displayed at G will be 2 Toposition 5 on G the number displayed at G will be 5 To position 6 on Gthe number displayed at G will be 8 To position 7 on G the numberdisplayed at G will be 1 To position 8 on G the number displayed at Gwill be 4 To position 9 on G the number displayed at G will be 7 Theremainder 10 deriving from the multiplication by three of the digits 4,5 and 6 and the remainder 20 deriving from the multiplication by threeof the digits 7, 8 and 9 are transmitted to the switch group of adjacenthigher order in such fashion that, e.g., in the case of transfers fromC.U. to C.D., to the number defined by p I the principal switch G' ofthe order C.D. there corre sponds (i.e., is displayed) the last digit ofthe number which is three times the value of the number defined by G ofthat higher order, augmented by 1 when the carry is unity and augmentedby 2 when the carry is two. To this end the switches 6' and G;; of thegroup CD. are associated in the following manner:

For position 0 of G the number displayed at 6' is 1 (value displayableat G' plus 1) For position 1 of G the number displayed at G is 4 (valuedisplayable at 6' plus 1) For position 2 of G the number displayed at G'is 7 (value displayable at G plus 1) v For position 3 of G' the numberdisplayed at 6' is 0 (value displayable at G plus 1) For position 4 ofG' the number displayed at 6' is 3 (value displayable at G' plus 1) Forposition 5 of G the number displayed at G' is 6 (value displayable at G'plus 1) For position 6 of G;, the number displayed at G' is 9 (valuedisplayable at G' plus 1) For position 7 of G the number displayed atG';, is 2 (value display-able at G' plus 1) For position 8 of G thenumber displayed at G' is 5 (value displayable at G plus 1) For position9 of G' the number displayed at-G' is 8 (value displayable at G; plus 1)In the hundreds order of FIGURE 2, the displays at the switch G" arerelated in identical fashion to the positions of 6",.

In the tens order C.D. of FIGURE-3, the switches G and G'.; areassociated in the following fashion:

For position 0 of G';, the number displayed at G is 2 (value displayableat 6' plus 2) For position 1 of G the number displayed at 6' is 5 (valuedisplayable at G' plus 2) For position 2 of G the number displayed atG'.; is 8 (value displayable at G' plus 2) For position 3 of G' thenumber displayed ot G'., is 1 (value displayable at G' plus 2) Forposition 4 of G' the number displayed at GC; is 4 (value displayable at6' plus 2) For position 5 of G the number displayed at G, is 7 (valuedisplayable at G plus 2) For position 6 of G' the number displayed at G,is

(value displayable at G' plus 2) For position 7 of G' the numberdisplayed at G'.; is 3 (value displayable at 6' plus 2) For position 8of G' the number displayed at G.; is 6 (value displayable at 6' plus 2)For position 9 of G' the number displayed at G' is 9 (value displayableat 6' plus 2) In the hundreds order C.C. of FIGURE 2 the displays at theswitch G"., are related in identical fashion to the position of G" Theauxiliary switches G G" etc. are energized only when there is no carryfrom the switch group of arithmetically preceding order. This occursonly for the positions 0, 1, 2 and 3 of the principal switch of thatgroup of preceding order. Consequently the switch group of the unitsorder C.U. is electrically connected to the auxiliary switch G' of thetens order C.D. only for the positions 0, 1, 2 and 3 of G by means ofthe first four terminals on the auxiliary interconnection switch G inthe units order C.U.

The auxiliary switches G' and G" etc., are energized only when there isa carry or remainder of unity deriving from the switch group of thepreceding or lower order, which occurs only for the 4, 5 and 6 positionsof the principal switch of that group. Consequently the group ofswitches C.U. is electrically connected to the switch G' of the decadesorder C.D. only for the 4, 5 and 6 positions of G by means of the fifth,sixth and seventh terminals on switch G The switches G,, G, are providedfor cases in which the carry from the adjacent lower order is two. Theunits group is connected to 6' of the tens group C.D. only for the 7, 8and 9 positions of G by means of the three last terminals on G It isevident that in the example given in FIGURE 2 there are no switches Gand G in the group C.U. in view of the fact that there does not existany switch or switches of order below the units order C.U.

The apparatus shown in FIGURE 1 includes only a single interconnectionswitch G G' and G" per order of switches, whereas the apparatus shown inFIGURE 2 is provided with one interconnection switch for each auxiliaryswitch. This comes from the fact that the carries 0, 1 or 2 must beshiftable from one auxiliary switch to another within each group ofswitches.

Provision for such shift is made necessary by the fact that a carry froma lower order can give rise in its turn to a carry which, absent thecarry from the lower order, would not take place. For example to thefourth position 3 of the principal switch G there may correspond fordisplay as an answer digit either the value 9 at G' (if there is nocarry from the units order) or the value 0 at G' if there is a carry ofone from C.U. Again, setting of G in C.D. to its fourth position ofvalue 3, may call for display of 1 at-G (1 here being the last digit of11) if the carry from the CU. is 2.

Similarly, setting of G' to its seventh position of value 6, may callfor display of 8 at 6' (no carry from C.U.), of 9 at G' (last digit ofpartial product 18 plus carry of 1 from CU.) or of O at G (last digit of18 plus carry of 2 from C.U.). If it calls for display of 8 or of 9there will be a carry of 1 to take forward to C.C. If it calls fordisplay of 0, there will be a carry of two to take forward to C.C.

The carries to be transmitted to the adjacent higher order group beingunlike among the various auxiliary switches, it is necessary to providea separate interconnection switch for-each auxiliary switch. Thus forthe auxiliary switch G there is provided interconnection switch G Gconnects G to G7 for the O, 1, 2 and 3 positions of the principal switchG to G" for the positions 4, 5 and 6 of G and to 6",; for the positions7, 8 and 9 of G' For the auxiliary switch G' there is provided theinterconnection switch G which connects G to G" for the positions 0', land 2 of G' G also connects G' to G;; for the G, positions 3, 4, 5 and 6and to G., for the G' positions 7, 8 and 9. For the auxiliary switch Gthe-re is provided the interconnection switch G'.: which connects 6 4and G" for the G positions 0, 1 and 2 to G for the G' positions 3, 4 and5 and to G", for the G positions 6, 7, 8 and 9.

When there is a group of switches for the thousands orders C.M. higherthan the hundreds order C.C., the auxiliary switches are connected inidentical fashion to interconnection switches G G and G" Preferably,diodes as indicated at 44 are inserted into the conductors whichenergize the wipers of the interconnection switches of higher order fromthose of lower order so that such energization can occur only in thesense leading from lower to higher orders.

Referring against to FIGURE 2, the ganged switches of first, second andthird order are identified generally at 30, 32 and 34. Each includes, asin FIGURE 1, a ten position pointer 16, and at least one combination ofa ten position auxiliary switch for display of a product digit and a tenposition interconnection switch for the selection, in the ganged switchof next higher order, of display switches correctly reflecting the carryrequired to be taken from the lower order into that next higher order.As in FIGURE 1, the pointer and all wiper arms in each ganged switch arefixed relative to each other.

In the first order C.U. of FIGURE 2 there is one such combination,including auxiliary switch deck G for illumination of product digitdisplay lamps (not shown) and transfer switch deck G for selection inthe tens order ganged switch 32 of an auxiliary switch deck correctlyreflecting the carry required to be made into the second order.

In the ganged switch 32 of second order C.D. of FIG- URE 2, there arethree such combinations, G and G for zero carry from the units orderC.U., G' and G for unity carry from C.U., and G.; and G for two carryfrom C.U.

Similarly in FIGURE 2 the third or hundreds order C.C. includes threesuch combinations G G G" G" and G.;, G for zero, unity and two carriesrespectively from the tens order C.D.

The auxiliary switch decks G G G' 6' G" G" G".; are all ten positionswitches, controlling in each position the illumination of a productdigit display lamp (not shown in FIGURE 2) similar to the lamps 22 ofFIGURE 1. The indica associated with those display lamps are howeverindicated in FIGURE 2, adjacent the switch terminals 29. These indiciaare in every case those of the cardinal numbers 0 to 9 which representthe last digit of the sum of the product which is given by three timesthe value of the position of the pointer 16, plus the carry required tobe taken from the previous order by reason of the position of thepointer 16 in such previous order.

In FIGURE 2 for G 6' and G" these indicia numbers are 0, 3, 6, 9, 2, 5,8, 1, 4, 7, these being the last digits of the numbers which are threetimes the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. For 6' and G" in FIGURE2, the associated indicia numbers 1, 4, 7, 0, 3, 6, 9, 2, 5, 8 are thelast digits just referred to increased by a carry of unity. For 6' andG", they are 2, 5, 8, 1, 4, 7, O, 3, 6, 9, being the last digits justreferred to increased by a carry of two.

The transfer or interconnection switch decks G G' 6' 6' G" G" and G"have their terminals 24 divided into groups according to the value 0, 1or 2 of the second digit of the sum described in the next precedingparagraph hereof, and each of these groups 9 is connected in parallel tothe wiper of a separate auxiliary switch deck in the next higher order.

For display of the fourth order digit in the final product, which mayhave a value 0, 1 or 2, two indicia display lamps 36 and 38 areprovided. The first, displaying when lighted the indicium 1, isconnected between conductor 2 and the 5th, 6th and 7th terminals 24 ofG" the 4th through. 7th terminals 24 of G;;, and the 4th through 6thterminals 24 of G",:. The terminals 24 are here identified by theirordinal positions counting counterclockwise from the top in FIG. 2, itbeing noted that the first terminal 24 on each of G" 6",; and G isengaged by its wiper 26 when pointer 16 of switch 34 is in its zeroposition, and so on. The second lamp, identified at reference character38, displays when lighted the indicium 2 and is connected betweenconductor 2 and the 8th through 10th terminals 24 on each of 6",, and G"and between conductor 2 and the 7th through 10th terminals 24 on G" Inthe absence of a ganged switch for the fourth order, the first threeterminals of G" are left open.

FIG. 2 illustrates derivation of the product 504 of the number 168multiplied by 3. The lowest order digit 4 of the answer is displayed atthe lamp (not shown) which is in series with the ninth contact 20 of Gin C.U. The second lowest order digit of the answer is displayed at thelamp (not shown) which is in series with the seventh terminal 20 of G,in CD, the wiper 18 of G., being energized from the wiper 26 of G via aconductor 40 and a diode 44. The third digit of the answer is displayedat the lamp (not shown) which is in series with the second terminal 20of G.;, the wiper 18 of 6",; being energized from G' via a conductor 42.i

The apparatus schematically shown in FIGURE 3 has been constructed insuch a way as to effectuate division of an arbitrary number by two, thatis to say it effects the operation inverse to that effected by theapparatus shown in FIGURE 1.

In consequence, the apparatus in FIGURE 3 is so constructed as to beanalogous to that for multiplication already described, the connectionsbeing reversed. Thus the transfer of carries is effected from a group ofhigher order to a group of adjacent lower order, whereas in FIGURE 1 itis effected from a group of lower order to the adjacent group of higherorder.

Three ganged switches 50, 52 and 54 are provided, essentially similar tothe two ganged switches of FIG- URES 1 and 2. Each includes a principalswitch or switch deck for set up of a dividend digit, at least oneauxiliary- OR 0 OR 0+ 1;2 OR 1 OR 1+(1:2) OR 2 OR 3 OR 3+(1z2) OR 4Consequently the switches G and G and the display lamps of a given group(ignoring primes, which merely identify the order) are associated in thefollowing fashion:

The complementary operations not effected, such as for example theremainder 1:2 (in the embodiment of FIG- URE 3) are transmitted in theform of remainders such as 10:2 to the switch group of adjacent lowerorder in such a way that, for the number set upon the principal switchof the said lower order group there will be displayed, via the lampsassociated with an auxiliary switch of that adjacent lower order, thenumber which equals one half the number so set up in that lower order(ignoring a remainder of /2 if present), augmented by five.

To this end the switches G and G and the lamps 22 of G in each group(again ignoring primes) are associated in the following fashion:

0 at G requires display of 5 at G i.e., whole number portion of0:2+l0:2=5

l at G requires display of 5 at G i.e.,

portion of 1:2+10:2=5+1:2

2 at G requires display of 6 at G portion of 2:2+10:2=6-

3 at G requires display of 6 at G portion of 3:2+l0z2=6+1:2

4 at G requires display of 7 at G portion of 4z2+1012=7 5 at G requiresdisplay of 7 at G portion of 5:2+10:2=7+1:2

6 at G requires display of 8 at G portion of 6z2+l0z2=8 7 at 6,,requires display of 8 at G portion of7:2+10:2=8+1:2

at G requires display of 9 at G portion of 8:2+10:2=9

9 at G requires display of 9 at G i.e.,

portion of 9:2+10:2=9+1:2

The complementary operation 1:2 still not performed is transmitted inthe form of the remainder 10:2 to the group of switches of next lowerorder in the same manner as just described. a

The auxiliary switches G G 6" are energized only when there is noremainder coming from the switch group of arithmetically precedingorder, that is, in a case of division, from the adjacent higher order.This occurs only when the number set up at the principal switch in thathigher order is a multiple of two.

Consequently the auxiliary switch G in the units order C.U. iselectrically connected, at its movable index on wiper 18, to the switchgroup CD. in the tens requires display of O at G requires display of 0at G requires display of l at. G requires display of 1 at G requiresdisplay of 2 at G requires display of 2 at G requires display of 3 at Grequires display of 3 at G requires display of 4 at G requires displayof 4 at G whole number whole number whole number whole number wholenumber whole whole number whole number order for the positions 0, 2, 4,6and 8 of G in CD, by

means of five terminals 24 at the corresponding even positions on G Theauxiliary switch G in the units order C.U. is electrically connected atits wiper 18 to the switch group of the tens order CD. for the positions1, 3, 5, 7 and 9 of G by means of the five odd terminals 24 on switch G'The numbers displayed via the lamps 22 of switch G are in both C.U. andCD. the same as those 'displayable at G augmented by the remainder to becarried, i.e., 5.

The operation of the apparatus is as follows: If the number to bedivided by two is 273 for example, the digit 3 will be set up atprincipal units order switch G the digit 7 at the principal tens orderswitch G' and the digit 2 at the principal hundreds order switch G wholenumber number The rotating indices on the switches being within eachgroup fixed to a common shaft, the indices of the switches G2, G3 andGA; Gz, 6'3, and G'A; 6H2, 6H3 and GHA, take up positions correspondingto the indices of G 6' and G" This state of affairs is illustrated inFIGURE 3.

To the third position 2 on G there corresponds the third terminal oneach of G" and G as hereinabove explained. That is to say, when theindex or pointer on G" is on the third terminal of G" associated withthe digit 2, the index of G" is on the third terminal of G" this thirdterminal being connected to a lamp arranged to display the digit 1. Theindex of G" is on the third terminal of G" which is electricallyconnected to the wiper of the switch G' of adjacent lower order. The twoterminals of the lamp connected to the third terminal of G" beingconnected to the two terminals 2 and 6 of the source of voltage, thislamp is illuminated, displaying the digit 1, which is the highest orderdigit of the desired quotient 273/ 2.

To the eighth positon of value 7 on G there corresponds display of 3 via6' and of 8 via G as hereinabove described, and also energization of theeighth terminal on G' That is, the index of G being on eighth terminalof G; which is associated with the dividend digit 7, the index of G'will be on the eighth terminal of G This eighth terminal on G' isconnected to a lamp arranged to display the digit 3. Further, the indexof G is on the eighth terminal of G' this eighth terminal beingconnected to a lamp for display of the digit 8. The wiper index of G' isenergized, in the case assumed, from the third stationary contact of Gwhereas the wiper index of G' is not energized. Hence the lamp fordisplay of 3 connected to the eighth terminal of G will be lighted butno lamp associated with G' will be lighted. Further, the index of G ison the eighth terminal of G which is connected electrically to theswitch G of the adjacent 'order- C.U. The wiper of G in the adjacentlower uni-ts order C.U. is therefore energized. The consequence of theforegoing is that 3, the second digit of the desired quotient 273/2, isdisplayed by means of a lamp in series with the eighth stationaryterminal of switch G in the order CD.

To the fourth position 3 of switch G there corresponds, via the fourthterminal of G display of the digit 1, similarly display of the digit 6via G and energization of the fourth terminal of G That is to say thatthe index of G being on the fourth terminal of G (associated withdividend digit 3), the index of G is on the fourth terminal of G whichfourth terminal is connected to a lamp for display of digit one.Moreover the index of G is on the fourth terminal of G which fourthterminal is connected to a lamp for display of the digit 6. The index ofG is on the fourth terminal of G which is electrically connected to alamp 56 for display of the digit 5.

The auxiliary switch G being not energized via the interconnectingswitch G the lamp 22 connected to the fourth terminal of G cannot belighted.

The auxiliary switch G being fed via eighth terminal of G the terminalsof the lamp 22 connected to the fourth terminal G are connected to thevoltage source and this lamp will be lighted, displaying the digit 6.This is the third digit in the desired quotient 273/ 2.

The lamp 56 provided for display of the digit after the decimal pointbeing connected to the terminals of the source of voltage on the onehand directly and on the other hand through the fourth terminal of theinterconnection switch G this lamp will be lighted, displaying the digit5.

The result displayed is hence 136.5 which is one half of 273.

The apparatus schematically shown in FIGURE 4 is analogous to that justdescribed, set up however to effect division by 3.

As in the case of FIGURE 2 the lamps connected to the terminals of theauxiliary switches and fed by the latter for display of suitable digitshave not been shown for reasons of simplicity of the drawing. It willhence be supposed in the following description that each time such aterminal is energized, the corresponding lamp will be lighted.

The three digits making up the number to be divided by 3 are defined anddisplayed by means of principal switches G G and G" of FIGURE 4, theseswitches being identical to those having the same reference charactersin FIGURE 2.

These switches thus permit set up of the digits 0 to 9, whose divisionby three give the following quotients:

0:3:0 OR 0' 1:3: /2, OR 0-1-(123) 213: /3 OR 0+ 213) 323:3 OR 1 4:3=1 /sOR 1+(1:3) 5:3=1 /a OR 1+(2z3) 6:3:2 OR 2 7=3=2 /3 OR 2+ 1:3) 823=2% OR2+(223) 9:3:3 OR 3 Consequently the switches G and G in each group(again ignoring primes) are associated in the following fashion:

To the position of value 0 of G there corresponds'display of O at G bymeans of a lamp 22 To the position of value 1 of G there play of 0 at Gby means of a lamp 22 To the position of value 2 of G there play of 0 atG by means of a lamp 22 To the position of value 3 of G there play of 1at G by means of a lamp 22 To the position of value 4 of G there play of1 at G; by means of a lamp 22 To the position of value 5 of G there playof 1 at G by means of a lamp 22 To the position of value 6 of G thereplay of 2 at G by means of a lamp 22 To the position of value 7 of Gthere play of 2 at G by means of a lamp 22 To the position of value 8 ofG there play of 2 at G by means of a lamp 22 To the position of value 9of G there play of 3 at G by means of a lamp 22 correspondsdiscorresponds discorresponds discorresponds discorrespondsdiscorresponds discorresponds discorresponds discorresponds dis- Thecomplementary operations 1:3 and 2:3 not yet carried out are transmittedto the switch group of adjacent lower order in the form of theremainders (10:3) or (20:3), according as the division operation beingperformed requires, in such fashion that for the number set up on theprincipal switch in the next lower order, there will be displayed, via alamp associated with an auxiliary switch of that adjacent lower order,the number which equals one third of the number so set up (ignoringremainders of /3 or /3 if present) augmented by or by as the case maybe.

To this end the switches G and G in each associated in the followingfashion:

group are Setting of G to position of value 0 requires at G display of 3derived from 0:3+10:3=3+l:3 Setting of G to position of value 1 requiresplay of 3 derived from l:3+l0:3=3+2:3 Setting of G to position of value2 requires play of 4 derived from 2z3+l0z3=4 Setting of G to position ofvalue 3 requires play of 4 derived from 3z3+l0:3=4+1:3 Setting of G toposition of value 4 requires play of 4 derived from 4:3+10:3=4+2:3Setting of G to position of value 5 requires play of 5 derived from5:3+10:3'=5 Setting of G to position of value 6 requires play of 5derived from.6:3+10:3=5+1:3

at G disat G disat G disat G disat G disat G3 dlS- 13 Setting of G toposition of value 7 requires. at G display of 5 derived from7:3+10:3=5+2:3 Setting of G to position of value 8 requires at G displayof 6 derived from 8:3+10:3=6 Setting of G to position of value 9requires at G display of 6 derived from 9:3+10:3=6+l:3

The complementary operations 1:3 and 2:3 are. trans mitted in the formsor remainders 10:3 or 20:3 according to the case to the switches ofadjacent lower order infashion similar already to that described.

Similarly the switches G and G within each group are associated in thefollowing fashion:

Setting of G to position of value requires at G, display of 6 derivedfrom 0: 3+20z3=6+2z3 Setting of G to position of value 1 requires playof 7 derived from 1:3+20:3=7 Setting of G to position of value 2requires play of7 derived from 2:3+20:3=7-|-1:3 Setting of G to positionof value 3 requires play of 7 derived from 3:3+20:3=7+2:3 Setting of Gto position of value 4 requires play of 8 derived from 4:3-|20:3=8Setting of G to position of value 5 requires play of 8 derived from5:3+20:3=8+1:3 Setting of G to position of value 6 requires play of 8derived from 6:3+20:3=8+2:3 Setting of G to position of value 7 requiresplay of 9 derived from 7a3+20z3=9 Setting of G to position of value 8requires play of 9 derived from. 8z3+20z3=9+123 Setting of G to positionof value 9 requires play of 9 derived from 9:3+20:3=9+2:3

The complementary operations 1:3 and 2:3 are as in the preceding casetransmitted to the switch of adjacent lower order in the form ofremainders 10":3 or 20:3 according to circumstance.

Switches G G and G" are not energized except in the case when theoperation being eifectuated in the adjacent higher order does not resultin a remainder. The switches G 6' and G" are not energized except whenthat operation includes a remainder of /3 and hence entails acomplementary operation 1:3, carried over in the form 10:3. Moreover theswitches G G'.; and G", are energized only when that operation includesa complementary operation 2:3 carried over under the form 20:3.

The carries to be transmitted from one group of switches to the nextbeing unlike for the various switches G G G in each group (contrary tothe situation in case of division by 2), it is necessary as in the caseof multiplication by 3 (FIGURE 2) to provide as many interconnectionswitches G G G etc. as there are auxiliary switches G G G In FIG. 4, theswitches have been set up to perform division by three of the dividend532, as is apparent from the settings of pointers G G, and G The answer177.3 is displayed at the lamps 22 (not shown in FIG- URE 4) connectedto the 6th terminal 20 of G" to at G; disat G, disat G 'disat G; disat6., disat. 6.; dis

at G; disat G, disat G4 the 4th terminal 20 of G to the 3rd terminal 20of G and at a lamp 60 arranged to display the digit 3, which isconnected to the third, sixth and ninth terminals 24 of G For otherdividend numbers whose quotients include a remainder of in the unitsorder, there is provided a lamp 62, arranged to display the digit 7.Lamp 62 is connected between voltage source terminal 2 and the first,fourth, seventh and tenth terminals 24 Of GC.

The diagram of FIGURE 5 represents a modification of the apparatus shownin FIGURE 3, operating by means of pulses.

In the apparatus of FIGURE 5 the switches are employed not to displaythe digits of the number representing the result of the operation butto' direct toward totalizers, via as many channels as there are digitsin that number, numbers of electric pulses equal to the values of thosedigits.

The diflFerent digits making up the number to be divided by 2 are set upand displayed by means of principal switches or pointers G G 6",, whichmay be identical to the pointers G 6' and G" hereinabove described.

The switches or pointers G 6' and G" are respectively associated withauxiliary switches G G G" in the same fashion as that described withreference to FIGURE 3, except that the terminals 20 of the switches G Gand G" are not provided for the illumination of lamps for display of thedigits of the answer but rather for the delivery to totalizat'ors 64, 66and 68 of pulses in number equal to the value of the answer digits.

To this end the terminals 20 ofG 6' and G" for the zero position of thepointers G G and G,, i.e. those corresponding to the digit zero, receiveno pulses Whatever. The terminals thereof corresponding to the digit onereceive one pulse, the terminals corresponding to the terminal tworeceive two pulses, and so on.

These pulses may be derived from separate sources of pulses.

They may for example be derived from a plurality of pulse transmittersone of which develops only one pulse, the others putting out two pulses,three pulses, four pulses and so on. Alternately they may come from asingle pulse transmitter putting out a continuous series of pulsesdistributed via a pulse distributor such as a ring counter for example,in such fashion that the channel which connects the number 1 terminalswill transmit only one pulse while the channel connecting the number 2terminals will transmit two pulses, and so on.

In the example illustrated in the FIGURE 5 a pulse source is shown at59. The source 59, which may be energized by a suitable control to gothrough a single cycle of operation on command after the dividend digitshave been set up at the pointers G 6' and G" is so constructed that whenthus energized it will go through a single cycle in which it deliversone pulse to a line a, two pulses to a line b, three pulses to a line 0,four pulses to a line d and five pulses to a line 2. These lines a to eare connected, as indicated in the drawing, to the terminals 20 of G Gand G" so as to supply to those terminals pulses in numbers equal to thequotient values of those terminals respectively.

Thus as already explained in detail with reference to FIGURE 3 thecomplementary operations (12) not effected in each stage must, whenrequired by the odd value of the dividend digit in such stage, betransmitted in the form of a remainder (10:2) to the switches ofadjacent lower order in such fashion that to the number set up at theprincipal switch of said lower order there corresponds a number ofpulses representative of the sub-multiple by two of the numbers so setup, augmented by 10:2, i.e., by five pulses.

To this end the interconnection switches G G and G-" receive five pulsesfrom line e at their wipers 26 and each time that the carry (10:2) mustbe etfectuated, these five pulses are transmitted to the pulse totalizerof adjacent lower order where they are added to those-trans.- mitted viathe auxiliary switch of that adjacentwlower order. To that end theterminals 24 at odd-valued positions 1, 3, 5, 7 and 9 in each of theinterconnection switches G G and G are connected to the pulse input ofthe totalizator of adjacent lower order.

The operation of the apparatus is as follows: Let it be supposed thatthe number to be divided by 2 is 327.

The digit 3 is set-up on the principal switch G. the digit 2 on switchG' and 7 on the switch G The rotating wiper contacts 18 and 26 and thepointer 16 being within each group mounted on a common axis, the wipersof G and G G' and G G" and 6",; take up positions corresponding to thoseof the pointers G G and G" 4 To the fourth position of G], of value 3,there corresponds the quotient digit 1 at G as hereinabove explainedwith reference to FIGURE 3, and also the fourth terminal of G" That isto say, the index of G" being on the fourth terminal of G marked 3, thewiper of G" will be located on the fourth terminal of G;. This fourthterminal of G" is connected to line a of the system and hence receivesone pulse. The pulse totalizator 64 connected to the wiper 18 of Gtherefore receives one pulse via wiper 18 of G" and causes this numberof pulses to be displayed in an appropriate manner, for example, bymeans of display lamps. The wiper 26 of G being on the fourth terminal24 of G the five pulses delivered from line a to wiper 26 aretransmitted, via a conductor 67, to the output conductor 69 of theauxiliary switch G';,, of adjacent lower order. These five pulsesdelivered from line e to wiper 26 of G" will be transmitted to the pulsetotalizator 66 which receives pulses from G' To the third position ofvalue 2 at G' there corresponds a unity quotient value at 6' ashereinabove described with reference to FIGURE 3, and also the thirdterminal of G' That is to say that, the index 16 of G, being on thethird terminal of G' representative of the digit 2, the index of theauxiliary switch G' is located on the third terminal of G' this thirdterminal being connected to the channel a which delivers one pulse fromthe source 59. This pulse is transmitted to the pulse totalizator 66connected to the output of G This pulse totalizator hence receives onepulse from G and five ulses from G' a total of six puses, and displaysthe number of pulses received in any suitable manner, for example bymeans of display lamps. The index of G' being on the third terminal of Gwhich is not connected to any conductor, the interconnection switch G'will hence deliver no pulses to the output line 70 of the auxiliaryswitch G of adjacent lower order.

To the digit 7 at the eighth position of G there corresponds a quotientvalue of three at G as hereinabove described with reference to FIGURE 3,and also the 8th terminal of G That is to say that, the index 16 of Gbeing on the 8th terminal, representative of the digit 7, the index 18of the auxiliary switch G will be on the 8th terminal of the switch Gthis 8th terminal being connected to the channel which delivers threepulses. These three pulses are transmitted to the pulse totalizator 68coupled to the output of G This totalizator having received no pulsesfrom G' hence receives a total of three pulses and displays the numberof pulses thus received. The index of G which is connected to channel 2,will be disposed on its 8th terminal. The interconnection switch G isconnected at its odd-valued 2nd, 4th, 6th, 8th and 10th terminals 24 toa pulse totalizator 72 intended to display the remainder of the quotientin the units order. This totalizator 72 hence receives five pulses fromthe 8th terminal of G and displays the number of pulses received.

The result displayed is hence 163.5.

From the foregoing description it will be apparent that the presentinvention provides apparatus for effecting, in a number system of basen, which may be base ten, multiplication of a plural digit number byanother number m. The multiplier is to be understood in a generic senseas including not only, for example in the decimal system, the digits 1to 9, but also the reciprocals 1, 1/2, 1/9 thereof, whereby division maybe effected in accordance with the invention. This apparatus comprises aplurality of groups of switches, one for each of a plurality of orderssuch as the orders CD. and C.C. in the plural digit multiplicand numberto be multiplied. Each of these groups of switches includes at least onepair of n-position switches such as, in FIGURES 1 and 2 the pair G G' ofCD. and the pair G" G of C.C., or in FIGURES 3, 4 and the pairs G G andG' G One switch G G or G of these pairs has associated therewith meansfor displaying, upon energization of that one switch,

one of the numbers 0, 1, 2, nl according to the position of such switch.In FIGURES 1 to 4, these display means are the lamps 22 and associatedindicia while in FIGURE 5 these display means are the pulse source 59,lines a to e, and totalizer or pulse counter 64 or 66. Moreover, thereare associated with the other switch G G or (3",, of each pair means foreffecting, according to the position of such other switch, energizationof a selected pair of switches in a group of adjacent order. Preferablyof course all switches of each group are ganged together to occupy thesame position. On multiplication, this adjacent order is the next higherorder whereas on division it is the next lower order. This energizationis effected via conductors such as the conductors 4G and 42 of FIGURE 3and the similar inter-order conductors shown in the other figures.

In a case of multiplication, the display means effect display for eachposition of the one switch such as G G or G" of the lowest order digitin the sum (km-l-p) wherein k is the order of that position in theseries 0, 1, 2, 11-1 and wherein p is the second lowest order digit inthe corresponding sum (km-l-p) in the adjacent lower order. In addition,in a case of multiplication, there are associated with the other switchG G or G of each of these pairs means for energizing in the adjacenthigher order the switches of a selected pair of switches in thatadjacent higher order according to the value of the second lowest orderdigit in the sum (km-j-p) first-named above.

In a case of division, the display means effect display, for eachposition of the one switch G G or G" of the units order digit in thepartial quotient (jn+lc) /m wherein k is the order of that position inthe series 0, 1, 2, n-l and wherein j is a number from 0 to nl equal tothe remainder in the corresponding partial quotient (jn+k)/m obtained inthe adjacent higher order. In addition, in a case of division, there areassociated with the other switch G G or G" of each of these pairs meansfor energizing in the adjacent lower order, according to the value ofthe remainder in said first-named partial quotient (jn+k)/m, theswitches of the one such pair in said adjacent lower order wherein j isequal to said last-named remainder.

It is evident that the invention is not limited to the case where theoutput channels of the auxiliary switches G G g and G" are connected topulse totalizators. Such an arrangement can be applied to any systemoperating as a function of the number of pulses received and in whichfor any desired reason it is desired to divide by two the number ofpulses.

It is moreover evident that the various circuits shown in FIGURES 1, 2,3, 4 and 5, are only exemplary of the invention and that in particularthe number of groups of switches is not in any way limited and that thefactor of multiplication may be different from two or three. Moregenerally, while the invention has been described herein in terms of anumber of examples, the invention is not limited thereto, the scope ofthe invention being rather set forth in the appended claims.

We claim:

1. Apparatus for deriving in a number system of base It the product of aplural digit number and a factor selected from the group consisting ofthe numbers m and l/m, where m is any integer greater than zero, saidapparatus comprising a plurality of groups of switches, one for eachorder of said plural digit number, each of said groups including atleast one pair of switches 'having 11 positions 0, 1, 2, n-l, theswitches of each of said groups being coupled together to occupy thesame position in the order 0, 1, 2, n-1, means associated with oneswitch in each of said pairs to display for each position of said oneswitch that integral portion of the product of said plural digit numberand the said factor which is of order corresponding to the orderassociated with said one switch, and means associated with the otherswitch of said pair for energizing in an adjacent order of switches aswitch selected according to the value of any undisplayed portion of theproduct resulting from positioning of said one switch.

2. Apparatus for effecting in a number system of base n themultiplication of a plural digit number by a numher In, said apparatuscomprising a plurality of groups of switches, one for each of aplurality of orders in said first number, each of said groups includingat least one pair of switches each having it positions 0, 1, 2, n- 1,the switches of each of said groups being coupled together to occupy thesame position in the order 0, 1, 2, n1, means associated with one switchin each of said pairs to display for each position of said one switch,upon energization of the switches of said pair, the value of the lowestorder digit in the sum (km-I-p) wherein k is the order of such positionin the series 0, 1, 2, n+1, and p is the second order digit in thecorresponding surn (km-j-p) in the adjacent lower order, and meansassociated with the other switch of said pair for energizing a selectedone of said pairs in the adjacent higher order according to the value ofthe second lowest order digit in the said first-named sum (km-j-p).

3. Apparatus according to claim 2 wherein n has the value ten.

4. Apparatus for effecting in a number system of base n the division ofa plural digit number by a number m, said apparatus comprising aplurality of groups of switches, one for each of a plurality of ordersin said first number, each of said groups including at least one pair ofswitches having 11 positions 0, 1, 2, n-l,

the switches of each of said groups being coupled together to occupy thesame position in the order 0, 1, 2, n1, means associated wit-h oneswitch in each of said pairs to display for each position of said oneswitch, upon energization of the switches of said pair, the value of theunits order digit in the partial quotient (jn+k)/m wherein k is theorder of said position in the series 0, 1, 2, n-1 and wherein j is anumber from 0 to n1 equal to'the remainder in the corresponding partialquotient (jn+k)/m obtained in the adjacent higher order, and meansassociated with the other switch of said pair for energizing in theadjacent lower order, according to the value of the remainder in saidfirst-named partial quotient (jn+k)/m, the switches of the one such pairin said adjacent lower order wherein j is equal to said last-namedremainder.

5. Apparatus according to claim 4 wherein n has the value ten.

6. Apparatus according to claim 1 wherein n has the value ten.

7. Apparatus for effecting in a number system of base n themultiplication of a plural digit number by another number, saidapparatus comprising a plurality of groups of switches, one for each ofa plurality of orders in said number, each of said groups including atleast one pair of n-position switches, the switches of each of saidgroups being coupled together to occupy the same position in the order0, 1, 2, n-1, means associated with one switch of each of said pairs fordisplaying, upon energization of said oneswitch, one of the numbers 0,1, 2, n1 according to the position of such switch, and means associatedwith the other switch of said pair for elfecting, according to theposition of said other switch, energization of a selected pair ofswitches in a group of adjacent order.

8. Apparatus according to claim 7 wherein n has the value ten.

9. Apparatus for deriving, in a number system of base n, the product ofa plural digit number and a factor selected from the group consisting ofthe numbers m and l/m, where m is any integer between 1 and n1, saidapparatus comprising a plurality of groups of switches, one for each ofa plurality of orders in said plural digit number, each of said groupsincluding at least one pair of n-position switches, the switches of eachof said groups being coupled together to occupy the same position in theorder 0, 1, 2, n1, means to supply to one switch of each of said pairsunlike numbers of pulses according to the position of said one switch,means to supply to the other switch of each of said pairs other unlikenumbers of pulses according to the position of said other switch, apulse counter connected to each of said one switches, and means couplingeach of said other switches to the pulse counter connected to the saidone switch in another one of said groups.

'10. Apparatus according to claim 9 wherein n has the value ten.

References Cited by the Examiner UNITED STATES PATENTS 2,131,908 10/1938Torkelson 235161 2,178,951 11/1939 Bryce 235161 2,23 6,794 4/1941 Furber235163 2,493,862 1/1950 Durfce 235163 2,986,333 5/1961 Thomas 2353,015,442 1/1962 Dickinson 235160 ROBERT C. BAILEY, Primary Examiner.

MALCOLM A. MORRISON, IRVING L. SRAGOW, Examiners. M. A. LERNER,Assistant Examiner.

4. APPARATUS FOR EFFECTING IN A NUMBER SYSTEM OF BASE N THE DIVISION OFA PLURAL DIGIT NUMBER BY A NUMBER M, SAID APPARATUS COMPRISING APLURALITY OF GROUPS OF SWITCHES, ONE FOR EACH OF A PLURALITY OF ORDERSIN SAID FIRST NUMBER, EACH OF SAID GROUPS, INCLUDING AT LEAST ONE PAIROF SWITCHES HAVING N POSITION 0, 1, 2, ... N-1, THE SWITCHES OF EACH OFSAID GROUPS BEING COUPLED TOGETHER TO OCCUPY THE SAME POSITION IN THEORDER O, 1, 2, ... N-1, MEANS ASSOCIATED WITH ONE SWITCH IN EACH OF SAIDPAIRS TO DISPLAY FOR EACH POSITION OF SAID ONE SWITCH, UPON ENERGIZATIONOF THE SWITCHES OF SAID PAIR, THE VALUE OF THE UNITS ORDER DIGIT IN THEPARTIAL QUOTIENT (JN+K)/M WHERENIN K IS THE ORDER OF SAID POSITION INTHE SERIES 0, 1, 2, ... N-1 AND WHEREIN J IS A NUMBER FROM 0 TO N-1EQUAL TO THE REMAINDER IN THE CORRESPONDING PARTIAL